Baoyan Li

An improved IMPES method for two-phase flow in porous media

In this paper we develop and numerically study an improved IMPES method for solving a partial differential coupled system for two-phase flow in a three-dimensional porous medium. This improved method utilizes an adaptive control strategy on the choice of a time step for saturation and takes a much larger time step for pressure than for the saturation. Through a stability analysis and a comparison with a simultaneous solution method, we show that this improved IMPES method is effective and efficient for the numerical simulation of two-phase flow and it is capable of solving two-phase coning problems.

The sequential method for the black-oil reservoir simulation on unstructured grids

This paper presents new results for applying the sequential solution method to the black-oil reservoir simulation with unstructured grids. The fully implicit solution method has been successfully applied to reservoir simulation with unstructured grids. However, the complexity of the fully implicit method and the irregularity of the grids result in a very complicated structure of linear equation systems (LESs) and in high computational cost to solve them. To tackle this problem, the sequential method is applied to reduce the size of the LESs. To deal with instable problems caused by the low implicit degree of this method, some practical techniques are introduced to control convergence of Newton-Raphsons iterations which are exploited in the linearization of the governing equations of the black-oil model. These techniques are tested with the benchmark problem of the ninth comparative solution project (CSP) organized by the society of petroleum engineers (SPE) and applied to field-scale models of both saturated and undersaturated reservoirs. The simulation results show that the sequential method uses as little as 20.01% of the memory for solving the LESs and 23.89% of the total computational time of the fully implicit method to reach the same precision for the undersaturated reservoirs, when the same iteration control parameters are used for both solution methods. However, for the saturated reservoirs, the sequential method must use stricter iteration control parameters to reach the same precision as the fully implicit method.

Control volume function approximation methods and their applications to modeling porous media flow

Abstract In this paper we introduce a new control volume method for the discretization of a partial differential equation. The interpolation in this method utilizes ‘bilinear’, spline, or weighted distance functions. We call this new method the control volume function approximation (CVFA) method. It can accurately approximate both the pressure and velocity in the simulation of multiphase flow in porous media, effectively reduce grid orientation effects, and be easily applied to arbitrarily shaped control volumes. It is suitable for hybrid grid porous media simulations. In this paper we focus on its development, numerical study, and comparison with a standard control volume finite element method. A two-phase incompressible flow problem is used to show the efficiency and accuracy of the CVFA.

The hp version of Eulerian-Lagrangian mixed discontinuous finite element methods for advection-diffusion problems

We study the hp version of three families of Eulerian-Lagrangian mixed discontinuous finite element (MDFE) methods for the numerical solution of advectiondiffusion problems. These methods are based on a space-time mixed formulation of the advection-diffusion problems. In space, they use discontinuous finite elements, and in time they approximately follow the Lagrangian flow paths (i.e., the hyperbolic part of the problems). Boundary conditions are incorporated in a natural and mass conservative manner. In fact, these methods are locally conservative. The analysis of this paper focuses on advection-diffusion problems in one space dimension. Error estimates are explicitly obtained in the grid size h, the polynomial degree p, and the solution regularity; arbitrary space grids and polynomial degree are allowed. These estimates are asymptotically optimal in both h and p for some of these methods. Numerical results to show convergence rates in h and p of the Eulerian-Lagrangian MDFE methods are presented. They are in a good agreement with the theory.